Decentralized Interaction and Co-Adaptation in the Repeated Prisoner&2018;s Dilemma

A Prisoner&2018;s dilemma that is repeated indefinitely has many equilibria; the problem of selecting among these is often approached using evolutionary models. The background of this paper is a number of earlier studies in which a specific type of evolutionary model, a genetic algorithm (GA), was used to investigate which behavior survives under selective pressure. However, that normative instrument searches for equilibria that may never be attainable. Furthermore, it aims for optimization and, accordingly, says what people should do to be successful in repeated prisoner&2018;s dilemma (RPD) type situations. In the current paper, I employ simulation to find out what people would do, whether this makes them successful or not. Using a replication of Miller&2018;s (1988) GA study for comparison, a model is simulated in which the population is spatially distributed across a torus. The agents only interact with their neighbors and locally adapt their strategy to what they perceive to be successful behavior among those neighbors. Although centralized GA-evolution may lead to somewhat better performance, this goes at the cost of a large increase in required computations while a population with decentralized interactions and co-adaptation is almost as successful and, additionally, endogenously learns a more efficient scheme for adaptation. Finally, when the agents&2018; perceptive capabilities are limited even further, so that they can only perceive how their neighbors are doing against themselves, rather than against all those neighbors&2018; opponents&2014;which essentially removes reputation as a source of information&2014;cooperation breaks down.     

Self-Assembling Sieves

A modular strategy has been applied to synthesize large, porous, self-assembling capsules. The coupling of tricyclic building blocks incorporating glycoluril hydrogen-bonding units and derivatives of triethylbenzene produces monomers which readily form homo- and heterodimeric assemblies (calculated structure is shown). Large guests can be trapped while small solvent molecules flow freely through the pores of the capsules.     

Submillimeter ESR spectra of Fe<Superscript>2+</Superscript> ions in synthetic and natural beryl crystals

Electron spin resonance spectra of non-Kramers bivalent iron (Fe²⁺) ions have been detected in synthetic and natural beryl crystals with an iron impurity. The observed ESR spectra have been attributed to resonance transitions of Fe²⁺ ions from the ground (singlet) state to excited (doublet) levels with the splitting Δ = 12.7 cm^–1 between the levels. The experimental angular and frequency dependences of the resonance field of the ESR signal have been described by the spin Hamiltonian with the effective spin S = 1. The analysis of the ESR data and optical absorption spectra indicates that the Fe²⁺ ions are situated in tetrahedral positions and substitute Be²⁺ cations in the beryl structure.     

Mesoscopic Fluctuations for the Thinned Circular Unitary Ensemble

In this paper we study the asymptotic behavior of mesoscopic fluctuations for the thinned Circular Unitary Ensemble. The effect of thinning is that the eigenvalues start to decorrelate. The decorrelation is stronger on the larger scales than on the smaller scales. We investigate this behavior by studying mesoscopic linear statistics. There are two regimes depending on the scale parameter and the thinning parameter. In one regime we obtain a CLT of a classical type and in the other regime we retrieve the CLT for CUE. The two regimes are separated by a critical line. On the critical line the limiting fluctuations are no longer Gaussian, but described by infinitely divisible laws. We argue that this transition phenomenon is universal by showing that the same transition and their laws appear for fluctuations of the thinned sine process in a growing box. The proofs are based on a Riemann-Hilbert problem for integrable operators.     

Solid state field-assisted diffusion of silver in multi-component tellurite glasses

In this work, we have prepared Ag-doped multi-component tellurite glasses by solid state electric field-assisted (SSFA) diffusion. The silver concentration profiles after SSFA diffusion were measured by secondary ion mass spectrometry (SIMS). It is found that the SIMS depth profiles can be well fitted by a classical erfc-like function. And the concentration dependence of silver diffusion coefficient has been investigated by using the Boltzmann-Matano analysis. The refractive index after SSFA diffusion is increased by ?n = 0.025 (λ = 1550 nm) without the glass surface being contaminated. Our results demonstrate that SSFA diffusion is a well controllable, non-destructive method to fabricate planar waveguides based on our newly developed tellurite glasses.     

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170)proposed an alternating iterative method for solving Cauchyproblems for general strongly elliptic and formally self-adjointsystems. However, in many applied problems, operators appearthat do not satisfy these requirements, e.g. Helmholtz-typeoperators. Therefore, in this study, an alternating procedurefor solving Cauchy problems for self-adjoint non-coercive ellipticoperators of second order is presented. A convergence proofof this procedure is given.     

Essential spectrum of difference operators on periodic metric spaces

The paper deals with the study of Fredholm property and essential spectrum of general difference (or band) operators acting on the spaces l ^p (X) on a discrete metric space X periodic with respect to the action of a finitely generated discrete group. The Schrödinger operator on a combinatorial periodic graph is a prominent example of a band operator of this kind.     

Reduced Weyl asymptotics for pseudodifferential operators on bounded domains II. The compact group case

Let G⊂O(n) be a compact group of isometries acting on n-dimensional Euclidean space Rn, and X a bounded domain in Rn which is transformed into itself under the action of G. Consider a symmetric, classical pseudodifferential operator A₀ in L²(Rn) that commutes with the regular representation of G, and assume that it is elliptic on X. We show that the spectrum of the Friedrichs extension A of the operator is discrete, and using the method of the stationary phase, we derive asymptotics for the number Nχ(λ) of eigenvalues of A equal or less than λ and with eigenfunctions in the χ-isotypic component of L²(X) as λ→∞, giving also an estimate for the remainder term for singular group actions. Since the considered critical set is a singular variety, we recur to partial desingularization in order to apply the stationary phase theorem.